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A consistent reduced-speed-of-light formulation of cosmic ray transport valid in weak- and strong-scattering regimes

Hopkins, Philip F. and Squire, Jonathan and Butsky, Iryna S. (2022) A consistent reduced-speed-of-light formulation of cosmic ray transport valid in weak- and strong-scattering regimes. Monthly Notices of the Royal Astronomical Society, 509 (3). pp. 3779-3797. ISSN 0035-8711. doi:10.1093/mnras/stab2635.

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We derive a consistent set of moment equations for cosmic ray (CR)-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts, we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is valid in both the nearly isotropic DF and/or strong-scattering regimes, and the arbitrarily anisotropic DF or free-streaming regimes, as well as allowing for anisotropic scattering and transport/magnetic field structure. We present the appropriate two-moment closure and equations for various choices of evolved variables, including the CR phase space DF f, number density n, total energy e, kinetic energy ϵ, and their fluxes or higher moments, and the appropriate coupling terms to the gas. We show that this naturally includes and generalizes a variety of terms including convection/fluid motion, anisotropic CR pressure, streaming, diffusion, gyro-resonant/streaming losses, and re-acceleration. We discuss how this extends previous treatments of CR transport including diffusion and moment methods and popular forms of the Fokker–Planck equation, as well as how this differs from the analogous M1-RHD equations. We also present two different methods for incorporating a reduced speed of light (RSOL) to reduce time-step limitations: In both, we carefully address where the RSOL (versus true c) must appear for the correct behaviour to be recovered in all interesting limits, and show how current implementations of CRs with an RSOL neglect some additional terms.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Hopkins, Philip F.0000-0003-3729-1684
Squire, Jonathan0000-0001-8479-962X
Butsky, Iryna S.0000-0003-1257-5007
Additional Information:© 2021 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2021 September 11. Received 2021 September 11; in original form 2021 March 15. Published: 02 October 2021. Support for PFH was provided by NSF Research Grants 1911233 and 20009234, NSF CAREER grant 1455342, and NASA grants 80NSSC18K0562 and HST-AR-15800.001-A. Numerical calculations were run on the Caltech compute cluster ‘Wheeler’, allocations FTA-Hopkins supported by the NSF and TACC, and NASA HEC SMD-16-7592. Support for JS was provided by Rutherford Discovery Fellowship RDF-U001804 and Marsden Fund grant UOO1727, which are managed through the Royal Society Te Apārangi. Data Availability: The data supporting this article are available on reasonable request to the corresponding author.
Group:Astronomy Department, TAPIR
Funding AgencyGrant Number
Royal Society Te ApārangiRDF-U001804
Royal SocietyUOO1727
Subject Keywords:MHD –plasmas –methods: numerical –cosmic rays –ISM: structure –galaxies: evolution
Issue or Number:3
Record Number:CaltechAUTHORS:20210323-112520656
Persistent URL:
Official Citation:Philip F Hopkins, Jonathan Squire, Iryna S Butsky, A consistent reduced-speed-of-light formulation of cosmic ray transport valid in weak- and strong-scattering regimes, Monthly Notices of the Royal Astronomical Society, Volume 509, Issue 3, January 2022, Pages 3779–3797,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108526
Deposited By: Tony Diaz
Deposited On:23 Mar 2021 19:04
Last Modified:14 Mar 2022 20:31

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